Finite Element Simulation Of Elastic Waves In 2-D Artificial Periodic Structures

In recent years,more and more studies have been done on vibration and noise reduction of honeycomb structures.The band gap characteristic of periodic structure can inhibit the propagation of fluctuation in band gap frequency range.Compared with the traditional vibration reduction method,these periodic structures do not need to add vibration reduction structure,and can use the structure itself to attenuate vibration.Therefore,the chiral structures with negative Poisson's ratio were studied and their band gap properties were calculated.Predecessors have studied the chiral structure with negative Poisson's ratio,calculated the band gap characteristics,and found that the ratio of the ligament length to the distance between adjacent central nodes(geometric configuration of the structure)is the key factor to determine whether the band gap is ideal.However,due to the geometric complexity of the chiral structure,modeling is complicated when calculating,the geometric configurations with ideal band gaps have not been obtained by predecessors.Therefore,this paper proposes a method that can effectively and quickly solve this problem.Keep the size of the cell of the geometric structure constant,given a central node size,a definite geometric configuration can be obtained.By calculating the band gap of different geometric configurations,the band gap of the whole structure can be obtained.By comparison,the geometric configuration with ideal band gap can be found.Firstly,several different chiral structures have been studied in this paper.The band gaps of the chiral structures under different geometries were calculated,and the variation of band gap with geometric configuration was obtained.It was found that the chiral structure of three ligaments has very good band gap characteristics compared to other chiral structures.Based on this result,the effect of symmetry on the band gap was studied,and the band gap of the improved vertical three ligaments was calculated.The calculation results show that increasing the axial symmetry while filling the center node can effectively improve the bandgap characteristics of the structure.Secondly,the frequency response function of different lattice structures is calculated,and the calculated results are consistent with the calculation results of band structures.Then the influence of period number on vibration attenuation is calculated,and it was found that the wider the band gap of the structure at the same cycle number,the greater the attenuation of the vibration.The chiral structure of the three ligaments and the vertical three ligaments structure have an ideal band gap width,which can effectively suppress the propagation of wave.Finally,the effect of symmetry on the vibration mode of primitive cell was analyzed.Then,the harmonic response of the structure under different frequencies is analyzed,and the displacement response of the structure under different frequency harmonic loads is observed,the accuracy of band structure and frequency response function curve is further verified.In addition,the transient fluctuation calculation was performed.The transient fluctuation of two structures with different band gaps is calculated.Comparing the displacement response of the two structures under the condition of the same source pulse.The calculation shows that the structure can effectively attenuate the multi-frequency vibration within the band gap.